detect.js

/*
<style>
#detect.child      > p,
#detect.firstchild p:first-child,
#detect.lastchild  p:last-child,
#detect.nthchild   p:nth-child(2n+1),
#detect.sibling    b + b        {display: block; width: 111px;}
</style>
*/

(function($) {

var tests = [
    {name: 'child', selector: '> p'},
    {name: 'firstchild', selector: '> p'},
    {name: 'lastchild', selector: '> p'},
    {name: 'nthchild', selector: '> p'},
    {name: 'sibling', selector: 'b + b'}
];

$.fn.detect = function() {

this.each(function() {
    var $element = $(this);
    $element.append('<div id="detect"><p><b>&nbsp</b><b>&nbsp;</b></p></div>');

    var $detect = $element.find('> #detect');

    for (var t in tests) {
        var test = tests[t];

        var name = test.name;
        var selector = test.selector;

        // remove existing and add the new one
        $detect.attr('class', name);

        if ($detect.find(selector).width() == 111) {
            $element.addClass(name);
        } else {
            $element.addClass('no-'+name);
        }
    }

    $detect.remove();
});

};
})(jQuery);

some.html

<script src="detect.js"></script>
<style>
#detect.child      > p,
#detect.firstchild p:first-child,
#detect.lastchild  p:last-child,
#detect.nthchild   p:nth-child(2n+1),
#detect.sibling    b + b        {display: block; width: 111px;}
</style>
<script>
$(document).ready(function() {
    var $body = $('body');
    $body.detect();

    var required = ['child', 'firstchild', 'lastchild', 'nthchild', 'sibling'];

    var failed = false;
    for (var r in required) {
        var klass = required[r];
        if (!$body.hasClass(klass)) {
            failed = true;
            break;
        }
    }

    if (failed) {
        $('#requirements-failed').css('display', 'block');
    } else {
        $('#requirements-succeeded').css('display', 'block');
    }
});
</script>